Which of the following are diamagnetic?

The correct options are
B $O_2^{2-}$
C $C_2$
D $L{i}_2$

This can be easily answered by apply Molecular Orbital Theory (MOT).

Species with odd number of electrons are definitely paramagnetic.

$N_2^{+}$ (Total electrons $=13$)

$\Rightarrow$It is paramagnetic

$C_2$ (Total electrons $=12$)

$\Rightarrow {\sigma }_{1s^2},{\sigma }_{1s^2}^{\ast },{\sigma }_{2s^2},{\sigma }_{2s^2}^{\ast },\left({\pi }_{2p_x^2}{\pi }_{2p_y^2}\right)$

It is diamagnetic

$O_2^{2-}$ (Total electrons $=18$)

$\Rightarrow {\sigma }_{1s^2},{\sigma }_{1s^2}^{\ast },{\sigma }_{2s^2},{\sigma }_{2s^2}^{\ast },{\sigma }_{2p_z^2},\left({\pi }_{2p_x^2}{\pi }_{2p_y^2}\right),\left({\pi }_{2p_x^2}^{\ast }{\pi }_{2p_y^2}^{\ast }\right)$

It is diamagnetic

${Li}_2$ (Total electrons $=6$)

$\Rightarrow {\sigma }_{1s^2},{\sigma }_{1s^2}^{\ast },{\sigma }_{2s^2}$

It is diamagnetic